Pump beginning to generate trickle of water (5)
I believe the answer is:
grill
'pump' is the definition.
(I've seen this before)
'beginning to generate trickle of water' is the wordplay.
'beginning to' says to take the initial letters.
'trickle of water' becomes 'rill' (I can't explain this - if you can you should believe this answer much more).
The first letter of 'generate' is 'g'.
'g'+'rill'='GRILL'
Can you help me to learn more?
(Other definitions for grill that I've seen before include "Means of cooking" , "Framework of metal bars" , "rack" , "Screen" , "Broil" .)